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Properties

Label 1200.4.a.p.1.1
Level $1200$
Weight $4$
Character 1200.1
Self dual yes
Analytic conductor $70.802$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1200,4,Mod(1,1200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1200.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1200.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(70.8022920069\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 120)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1200.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.00000 q^{3} +20.0000 q^{7} +9.00000 q^{9} +56.0000 q^{11} +86.0000 q^{13} +106.000 q^{17} -4.00000 q^{19} -60.0000 q^{21} +136.000 q^{23} -27.0000 q^{27} -206.000 q^{29} +152.000 q^{31} -168.000 q^{33} -282.000 q^{37} -258.000 q^{39} -246.000 q^{41} +412.000 q^{43} +40.0000 q^{47} +57.0000 q^{49} -318.000 q^{51} +126.000 q^{53} +12.0000 q^{57} -56.0000 q^{59} -2.00000 q^{61} +180.000 q^{63} -388.000 q^{67} -408.000 q^{69} +672.000 q^{71} -1170.00 q^{73} +1120.00 q^{77} -408.000 q^{79} +81.0000 q^{81} +668.000 q^{83} +618.000 q^{87} +66.0000 q^{89} +1720.00 q^{91} -456.000 q^{93} +926.000 q^{97} +504.000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.00000 −0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 20.0000 1.07990 0.539949 − 0.841698i \(-0.318443\pi\)
0.539949 + 0.841698i \(0.318443\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 56.0000 1.53497 0.767483 − 0.641069i \(-0.221509\pi\)
0.767483 + 0.641069i \(0.221509\pi\)
\(12\) 0 0
\(13\) 86.0000 1.83478 0.917389 − 0.397992i \(-0.130293\pi\)
0.917389 + 0.397992i \(0.130293\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 106.000 1.51228 0.756140 − 0.654409i \(-0.227083\pi\)
0.756140 + 0.654409i \(0.227083\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.0482980 −0.0241490 − 0.999708i \(-0.507688\pi\)
−0.0241490 + 0.999708i \(0.507688\pi\)
\(20\) 0 0
\(21\) −60.0000 −0.623480
\(22\) 0 0
\(23\) 136.000 1.23295 0.616477 − 0.787373i \(-0.288559\pi\)
0.616477 + 0.787373i \(0.288559\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −206.000 −1.31908 −0.659539 − 0.751671i \(-0.729248\pi\)
−0.659539 + 0.751671i \(0.729248\pi\)
\(30\) 0 0
\(31\) 152.000 0.880645 0.440323 − 0.897840i \(-0.354864\pi\)
0.440323 + 0.897840i \(0.354864\pi\)
\(32\) 0 0
\(33\) −168.000 −0.886214
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −282.000 −1.25299 −0.626493 − 0.779427i \(-0.715510\pi\)
−0.626493 + 0.779427i \(0.715510\pi\)
\(38\) 0 0
\(39\) −258.000 −1.05931
\(40\) 0 0
\(41\) −246.000 −0.937043 −0.468521 − 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 412.000 1.46115 0.730575 − 0.682833i \(-0.239252\pi\)
0.730575 + 0.682833i \(0.239252\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 40.0000 0.124140 0.0620702 − 0.998072i \(-0.480230\pi\)
0.0620702 + 0.998072i \(0.480230\pi\)
\(48\) 0 0
\(49\) 57.0000 0.166181
\(50\) 0 0
\(51\) −318.000 −0.873116
\(52\) 0 0
\(53\) 126.000 0.326555 0.163278 − 0.986580i \(-0.447793\pi\)
0.163278 + 0.986580i \(0.447793\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 12.0000 0.0278849
\(58\) 0 0
\(59\) −56.0000 −0.123569 −0.0617846 − 0.998090i \(-0.519679\pi\)
−0.0617846 + 0.998090i \(0.519679\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.00419793 −0.00209897 − 0.999998i \(-0.500668\pi\)
−0.00209897 + 0.999998i \(0.500668\pi\)
\(62\) 0 0
\(63\) 180.000 0.359966
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −388.000 −0.707489 −0.353744 − 0.935342i \(-0.615092\pi\)
−0.353744 + 0.935342i \(0.615092\pi\)
\(68\) 0 0
\(69\) −408.000 −0.711847
\(70\) 0 0
\(71\) 672.000 1.12326 0.561632 − 0.827387i \(-0.310174\pi\)
0.561632 + 0.827387i \(0.310174\pi\)
\(72\) 0 0
\(73\) −1170.00 −1.87586 −0.937932 − 0.346818i \(-0.887262\pi\)
−0.937932 + 0.346818i \(0.887262\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1120.00 1.65761
\(78\) 0 0
\(79\) −408.000 −0.581058 −0.290529 − 0.956866i \(-0.593831\pi\)
−0.290529 + 0.956866i \(0.593831\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) 668.000 0.883404 0.441702 − 0.897162i \(-0.354375\pi\)
0.441702 + 0.897162i \(0.354375\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 618.000 0.761570
\(88\) 0 0
\(89\) 66.0000 0.0786066 0.0393033 − 0.999227i \(-0.487486\pi\)
0.0393033 + 0.999227i \(0.487486\pi\)
\(90\) 0 0
\(91\) 1720.00 1.98137
\(92\) 0 0
\(93\) −456.000 −0.508441
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 926.000 0.969289 0.484645 − 0.874711i \(-0.338949\pi\)
0.484645 + 0.874711i \(0.338949\pi\)
\(98\) 0 0
\(99\) 504.000 0.511656
\(100\) 0 0
\(101\) −198.000 −0.195067 −0.0975333 − 0.995232i \(-0.531095\pi\)
−0.0975333 + 0.995232i \(0.531095\pi\)
\(102\) 0 0
\(103\) −1532.00 −1.46556 −0.732779 − 0.680467i \(-0.761777\pi\)
−0.732779 + 0.680467i \(0.761777\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −444.000 −0.401150 −0.200575 − 0.979678i \(-0.564281\pi\)
−0.200575 + 0.979678i \(0.564281\pi\)
\(108\) 0 0
\(109\) 62.0000 0.0544819 0.0272409 − 0.999629i \(-0.491328\pi\)
0.0272409 + 0.999629i \(0.491328\pi\)
\(110\) 0 0
\(111\) 846.000 0.723412
\(112\) 0 0
\(113\) −414.000 −0.344653 −0.172327 − 0.985040i \(-0.555128\pi\)
−0.172327 + 0.985040i \(0.555128\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 774.000 0.611593
\(118\) 0 0
\(119\) 2120.00 1.63311
\(120\) 0 0
\(121\) 1805.00 1.35612
\(122\) 0 0
\(123\) 738.000 0.541002
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −996.000 −0.695911 −0.347956 − 0.937511i \(-0.613124\pi\)
−0.347956 + 0.937511i \(0.613124\pi\)
\(128\) 0 0
\(129\) −1236.00 −0.843595
\(130\) 0 0
\(131\) 264.000 0.176075 0.0880374 − 0.996117i \(-0.471941\pi\)
0.0880374 + 0.996117i \(0.471941\pi\)
\(132\) 0 0
\(133\) −80.0000 −0.0521570
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2278.00 −1.42060 −0.710302 − 0.703897i \(-0.751442\pi\)
−0.710302 + 0.703897i \(0.751442\pi\)
\(138\) 0 0
\(139\) −1812.00 −1.10570 −0.552848 − 0.833282i \(-0.686459\pi\)
−0.552848 + 0.833282i \(0.686459\pi\)
\(140\) 0 0
\(141\) −120.000 −0.0716725
\(142\) 0 0
\(143\) 4816.00 2.81632
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −171.000 −0.0959445
\(148\) 0 0
\(149\) −1534.00 −0.843424 −0.421712 − 0.906730i \(-0.638571\pi\)
−0.421712 + 0.906730i \(0.638571\pi\)
\(150\) 0 0
\(151\) 3016.00 1.62542 0.812711 − 0.582668i \(-0.197991\pi\)
0.812711 + 0.582668i \(0.197991\pi\)
\(152\) 0 0
\(153\) 954.000 0.504094
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1814.00 0.922121 0.461060 − 0.887369i \(-0.347469\pi\)
0.461060 + 0.887369i \(0.347469\pi\)
\(158\) 0 0
\(159\) −378.000 −0.188537
\(160\) 0 0
\(161\) 2720.00 1.33147
\(162\) 0 0
\(163\) −1844.00 −0.886093 −0.443047 − 0.896499i \(-0.646102\pi\)
−0.443047 + 0.896499i \(0.646102\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3768.00 1.74597 0.872984 − 0.487749i \(-0.162182\pi\)
0.872984 + 0.487749i \(0.162182\pi\)
\(168\) 0 0
\(169\) 5199.00 2.36641
\(170\) 0 0
\(171\) −36.0000 −0.0160993
\(172\) 0 0
\(173\) −938.000 −0.412224 −0.206112 − 0.978528i \(-0.566081\pi\)
−0.206112 + 0.978528i \(0.566081\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 168.000 0.0713427
\(178\) 0 0
\(179\) −3968.00 −1.65688 −0.828442 − 0.560075i \(-0.810772\pi\)
−0.828442 + 0.560075i \(0.810772\pi\)
\(180\) 0 0
\(181\) −3514.00 −1.44306 −0.721529 − 0.692384i \(-0.756560\pi\)
−0.721529 + 0.692384i \(0.756560\pi\)
\(182\) 0 0
\(183\) 6.00000 0.00242368
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 5936.00 2.32130
\(188\) 0 0
\(189\) −540.000 −0.207827
\(190\) 0 0
\(191\) 1480.00 0.560676 0.280338 − 0.959901i \(-0.409554\pi\)
0.280338 + 0.959901i \(0.409554\pi\)
\(192\) 0 0
\(193\) 2774.00 1.03460 0.517298 − 0.855806i \(-0.326938\pi\)
0.517298 + 0.855806i \(0.326938\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3806.00 1.37648 0.688239 − 0.725484i \(-0.258384\pi\)
0.688239 + 0.725484i \(0.258384\pi\)
\(198\) 0 0
\(199\) 856.000 0.304926 0.152463 − 0.988309i \(-0.451280\pi\)
0.152463 + 0.988309i \(0.451280\pi\)
\(200\) 0 0
\(201\) 1164.00 0.408469
\(202\) 0 0
\(203\) −4120.00 −1.42447
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1224.00 0.410985
\(208\) 0 0
\(209\) −224.000 −0.0741359
\(210\) 0 0
\(211\) −3020.00 −0.985334 −0.492667 − 0.870218i \(-0.663978\pi\)
−0.492667 + 0.870218i \(0.663978\pi\)
\(212\) 0 0
\(213\) −2016.00 −0.648517
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3040.00 0.951008
\(218\) 0 0
\(219\) 3510.00 1.08303
\(220\) 0 0
\(221\) 9116.00 2.77470
\(222\) 0 0
\(223\) −1684.00 −0.505690 −0.252845 − 0.967507i \(-0.581366\pi\)
−0.252845 + 0.967507i \(0.581366\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2004.00 0.585948 0.292974 − 0.956120i \(-0.405355\pi\)
0.292974 + 0.956120i \(0.405355\pi\)
\(228\) 0 0
\(229\) −5042.00 −1.45496 −0.727478 − 0.686131i \(-0.759307\pi\)
−0.727478 + 0.686131i \(0.759307\pi\)
\(230\) 0 0
\(231\) −3360.00 −0.957021
\(232\) 0 0
\(233\) 3090.00 0.868810 0.434405 − 0.900718i \(-0.356959\pi\)
0.434405 + 0.900718i \(0.356959\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1224.00 0.335474
\(238\) 0 0
\(239\) −2136.00 −0.578102 −0.289051 − 0.957314i \(-0.593340\pi\)
−0.289051 + 0.957314i \(0.593340\pi\)
\(240\) 0 0
\(241\) 98.0000 0.0261939 0.0130970 − 0.999914i \(-0.495831\pi\)
0.0130970 + 0.999914i \(0.495831\pi\)
\(242\) 0 0
\(243\) −243.000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −344.000 −0.0886162
\(248\) 0 0
\(249\) −2004.00 −0.510033
\(250\) 0 0
\(251\) 5040.00 1.26742 0.633709 − 0.773571i \(-0.281532\pi\)
0.633709 + 0.773571i \(0.281532\pi\)
\(252\) 0 0
\(253\) 7616.00 1.89254
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1986.00 0.482036 0.241018 − 0.970521i \(-0.422519\pi\)
0.241018 + 0.970521i \(0.422519\pi\)
\(258\) 0 0
\(259\) −5640.00 −1.35310
\(260\) 0 0
\(261\) −1854.00 −0.439692
\(262\) 0 0
\(263\) 1416.00 0.331994 0.165997 − 0.986126i \(-0.446916\pi\)
0.165997 + 0.986126i \(0.446916\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −198.000 −0.0453835
\(268\) 0 0
\(269\) −6670.00 −1.51181 −0.755905 − 0.654681i \(-0.772803\pi\)
−0.755905 + 0.654681i \(0.772803\pi\)
\(270\) 0 0
\(271\) −48.0000 −0.0107594 −0.00537969 − 0.999986i \(-0.501712\pi\)
−0.00537969 + 0.999986i \(0.501712\pi\)
\(272\) 0 0
\(273\) −5160.00 −1.14395
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −6938.00 −1.50492 −0.752462 − 0.658636i \(-0.771134\pi\)
−0.752462 + 0.658636i \(0.771134\pi\)
\(278\) 0 0
\(279\) 1368.00 0.293548
\(280\) 0 0
\(281\) −1694.00 −0.359628 −0.179814 − 0.983701i \(-0.557550\pi\)
−0.179814 + 0.983701i \(0.557550\pi\)
\(282\) 0 0
\(283\) −6364.00 −1.33675 −0.668376 − 0.743824i \(-0.733010\pi\)
−0.668376 + 0.743824i \(0.733010\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4920.00 −1.01191
\(288\) 0 0
\(289\) 6323.00 1.28699
\(290\) 0 0
\(291\) −2778.00 −0.559619
\(292\) 0 0
\(293\) 3134.00 0.624881 0.312441 − 0.949937i \(-0.398853\pi\)
0.312441 + 0.949937i \(0.398853\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −1512.00 −0.295405
\(298\) 0 0
\(299\) 11696.0 2.26220
\(300\) 0 0
\(301\) 8240.00 1.57789
\(302\) 0 0
\(303\) 594.000 0.112622
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −236.000 −0.0438737 −0.0219369 − 0.999759i \(-0.506983\pi\)
−0.0219369 + 0.999759i \(0.506983\pi\)
\(308\) 0 0
\(309\) 4596.00 0.846140
\(310\) 0 0
\(311\) −3776.00 −0.688480 −0.344240 − 0.938882i \(-0.611863\pi\)
−0.344240 + 0.938882i \(0.611863\pi\)
\(312\) 0 0
\(313\) 7918.00 1.42988 0.714939 − 0.699187i \(-0.246454\pi\)
0.714939 + 0.699187i \(0.246454\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4362.00 −0.772853 −0.386426 − 0.922320i \(-0.626291\pi\)
−0.386426 + 0.922320i \(0.626291\pi\)
\(318\) 0 0
\(319\) −11536.0 −2.02474
\(320\) 0 0
\(321\) 1332.00 0.231604
\(322\) 0 0
\(323\) −424.000 −0.0730402
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −186.000 −0.0314551
\(328\) 0 0
\(329\) 800.000 0.134059
\(330\) 0 0
\(331\) −7980.00 −1.32514 −0.662569 − 0.749001i \(-0.730534\pi\)
−0.662569 + 0.749001i \(0.730534\pi\)
\(332\) 0 0
\(333\) −2538.00 −0.417662
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 8294.00 1.34066 0.670331 − 0.742062i \(-0.266152\pi\)
0.670331 + 0.742062i \(0.266152\pi\)
\(338\) 0 0
\(339\) 1242.00 0.198986
\(340\) 0 0
\(341\) 8512.00 1.35176
\(342\) 0 0
\(343\) −5720.00 −0.900440
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −964.000 −0.149136 −0.0745681 − 0.997216i \(-0.523758\pi\)
−0.0745681 + 0.997216i \(0.523758\pi\)
\(348\) 0 0
\(349\) 8670.00 1.32978 0.664892 − 0.746940i \(-0.268478\pi\)
0.664892 + 0.746940i \(0.268478\pi\)
\(350\) 0 0
\(351\) −2322.00 −0.353103
\(352\) 0 0
\(353\) 2314.00 0.348900 0.174450 − 0.984666i \(-0.444185\pi\)
0.174450 + 0.984666i \(0.444185\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −6360.00 −0.942876
\(358\) 0 0
\(359\) 1896.00 0.278738 0.139369 − 0.990240i \(-0.455493\pi\)
0.139369 + 0.990240i \(0.455493\pi\)
\(360\) 0 0
\(361\) −6843.00 −0.997667
\(362\) 0 0
\(363\) −5415.00 −0.782958
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1484.00 0.211074 0.105537 − 0.994415i \(-0.466344\pi\)
0.105537 + 0.994415i \(0.466344\pi\)
\(368\) 0 0
\(369\) −2214.00 −0.312348
\(370\) 0 0
\(371\) 2520.00 0.352647
\(372\) 0 0
\(373\) −12370.0 −1.71714 −0.858571 − 0.512694i \(-0.828648\pi\)
−0.858571 + 0.512694i \(0.828648\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −17716.0 −2.42021
\(378\) 0 0
\(379\) −5620.00 −0.761689 −0.380844 − 0.924639i \(-0.624367\pi\)
−0.380844 + 0.924639i \(0.624367\pi\)
\(380\) 0 0
\(381\) 2988.00 0.401784
\(382\) 0 0
\(383\) 5880.00 0.784475 0.392238 − 0.919864i \(-0.371701\pi\)
0.392238 + 0.919864i \(0.371701\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3708.00 0.487050
\(388\) 0 0
\(389\) 2082.00 0.271367 0.135683 − 0.990752i \(-0.456677\pi\)
0.135683 + 0.990752i \(0.456677\pi\)
\(390\) 0 0
\(391\) 14416.0 1.86457
\(392\) 0 0
\(393\) −792.000 −0.101657
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1742.00 0.220223 0.110111 − 0.993919i \(-0.464879\pi\)
0.110111 + 0.993919i \(0.464879\pi\)
\(398\) 0 0
\(399\) 240.000 0.0301129
\(400\) 0 0
\(401\) −3270.00 −0.407222 −0.203611 − 0.979052i \(-0.565268\pi\)
−0.203611 + 0.979052i \(0.565268\pi\)
\(402\) 0 0
\(403\) 13072.0 1.61579
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −15792.0 −1.92329
\(408\) 0 0
\(409\) −6134.00 −0.741581 −0.370791 − 0.928716i \(-0.620913\pi\)
−0.370791 + 0.928716i \(0.620913\pi\)
\(410\) 0 0
\(411\) 6834.00 0.820186
\(412\) 0 0
\(413\) −1120.00 −0.133442
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 5436.00 0.638374
\(418\) 0 0
\(419\) 10392.0 1.21165 0.605826 − 0.795597i \(-0.292843\pi\)
0.605826 + 0.795597i \(0.292843\pi\)
\(420\) 0 0
\(421\) −12690.0 −1.46906 −0.734528 − 0.678578i \(-0.762596\pi\)
−0.734528 + 0.678578i \(0.762596\pi\)
\(422\) 0 0
\(423\) 360.000 0.0413801
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −40.0000 −0.00453334
\(428\) 0 0
\(429\) −14448.0 −1.62600
\(430\) 0 0
\(431\) 7408.00 0.827914 0.413957 − 0.910297i \(-0.364146\pi\)
0.413957 + 0.910297i \(0.364146\pi\)
\(432\) 0 0
\(433\) 5062.00 0.561811 0.280906 − 0.959735i \(-0.409365\pi\)
0.280906 + 0.959735i \(0.409365\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −544.000 −0.0595493
\(438\) 0 0
\(439\) 7160.00 0.778424 0.389212 − 0.921148i \(-0.372747\pi\)
0.389212 + 0.921148i \(0.372747\pi\)
\(440\) 0 0
\(441\) 513.000 0.0553936
\(442\) 0 0
\(443\) 17100.0 1.83396 0.916981 − 0.398930i \(-0.130618\pi\)
0.916981 + 0.398930i \(0.130618\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 4602.00 0.486951
\(448\) 0 0
\(449\) 8634.00 0.907491 0.453746 − 0.891131i \(-0.350087\pi\)
0.453746 + 0.891131i \(0.350087\pi\)
\(450\) 0 0
\(451\) −13776.0 −1.43833
\(452\) 0 0
\(453\) −9048.00 −0.938437
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −2986.00 −0.305644 −0.152822 − 0.988254i \(-0.548836\pi\)
−0.152822 + 0.988254i \(0.548836\pi\)
\(458\) 0 0
\(459\) −2862.00 −0.291039
\(460\) 0 0
\(461\) −2406.00 −0.243077 −0.121539 − 0.992587i \(-0.538783\pi\)
−0.121539 + 0.992587i \(0.538783\pi\)
\(462\) 0 0
\(463\) −14316.0 −1.43698 −0.718489 − 0.695538i \(-0.755166\pi\)
−0.718489 + 0.695538i \(0.755166\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −292.000 −0.0289339 −0.0144670 − 0.999895i \(-0.504605\pi\)
−0.0144670 + 0.999895i \(0.504605\pi\)
\(468\) 0 0
\(469\) −7760.00 −0.764016
\(470\) 0 0
\(471\) −5442.00 −0.532387
\(472\) 0 0
\(473\) 23072.0 2.24282
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1134.00 0.108852
\(478\) 0 0
\(479\) −14056.0 −1.34078 −0.670391 − 0.742008i \(-0.733874\pi\)
−0.670391 + 0.742008i \(0.733874\pi\)
\(480\) 0 0
\(481\) −24252.0 −2.29895
\(482\) 0 0
\(483\) −8160.00 −0.768722
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −11204.0 −1.04251 −0.521254 − 0.853401i \(-0.674536\pi\)
−0.521254 + 0.853401i \(0.674536\pi\)
\(488\) 0 0
\(489\) 5532.00 0.511586
\(490\) 0 0
\(491\) −4608.00 −0.423536 −0.211768 − 0.977320i \(-0.567922\pi\)
−0.211768 + 0.977320i \(0.567922\pi\)
\(492\) 0 0
\(493\) −21836.0 −1.99482
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 13440.0 1.21301
\(498\) 0 0
\(499\) −2468.00 −0.221409 −0.110704 − 0.993853i \(-0.535311\pi\)
−0.110704 + 0.993853i \(0.535311\pi\)
\(500\) 0 0
\(501\) −11304.0 −1.00803
\(502\) 0 0
\(503\) 12192.0 1.08074 0.540372 − 0.841426i \(-0.318283\pi\)
0.540372 + 0.841426i \(0.318283\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −15597.0 −1.36625
\(508\) 0 0
\(509\) 1714.00 0.149257 0.0746284 − 0.997211i \(-0.476223\pi\)
0.0746284 + 0.997211i \(0.476223\pi\)
\(510\) 0 0
\(511\) −23400.0 −2.02574
\(512\) 0 0
\(513\) 108.000 0.00929496
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 2240.00 0.190551
\(518\) 0 0
\(519\) 2814.00 0.237998
\(520\) 0 0
\(521\) −18014.0 −1.51479 −0.757397 − 0.652955i \(-0.773529\pi\)
−0.757397 + 0.652955i \(0.773529\pi\)
\(522\) 0 0
\(523\) −16748.0 −1.40027 −0.700133 − 0.714013i \(-0.746876\pi\)
−0.700133 + 0.714013i \(0.746876\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16112.0 1.33178
\(528\) 0 0
\(529\) 6329.00 0.520178
\(530\) 0 0
\(531\) −504.000 −0.0411897
\(532\) 0 0
\(533\) −21156.0 −1.71926
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 11904.0 0.956602
\(538\) 0 0
\(539\) 3192.00 0.255082
\(540\) 0 0
\(541\) −14018.0 −1.11401 −0.557006 − 0.830508i \(-0.688050\pi\)
−0.557006 + 0.830508i \(0.688050\pi\)
\(542\) 0 0
\(543\) 10542.0 0.833150
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −412.000 −0.0322045 −0.0161022 − 0.999870i \(-0.505126\pi\)
−0.0161022 + 0.999870i \(0.505126\pi\)
\(548\) 0 0
\(549\) −18.0000 −0.00139931
\(550\) 0 0
\(551\) 824.000 0.0637089
\(552\) 0 0
\(553\) −8160.00 −0.627484
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18218.0 −1.38586 −0.692928 − 0.721007i \(-0.743679\pi\)
−0.692928 + 0.721007i \(0.743679\pi\)
\(558\) 0 0
\(559\) 35432.0 2.68088
\(560\) 0 0
\(561\) −17808.0 −1.34020
\(562\) 0 0
\(563\) 23524.0 1.76096 0.880478 − 0.474087i \(-0.157222\pi\)
0.880478 + 0.474087i \(0.157222\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1620.00 0.119989
\(568\) 0 0
\(569\) 23330.0 1.71888 0.859442 − 0.511234i \(-0.170811\pi\)
0.859442 + 0.511234i \(0.170811\pi\)
\(570\) 0 0
\(571\) 13124.0 0.961860 0.480930 − 0.876759i \(-0.340299\pi\)
0.480930 + 0.876759i \(0.340299\pi\)
\(572\) 0 0
\(573\) −4440.00 −0.323706
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −11714.0 −0.845165 −0.422582 − 0.906324i \(-0.638876\pi\)
−0.422582 + 0.906324i \(0.638876\pi\)
\(578\) 0 0
\(579\) −8322.00 −0.597324
\(580\) 0 0
\(581\) 13360.0 0.953987
\(582\) 0 0
\(583\) 7056.00 0.501252
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17628.0 −1.23950 −0.619749 − 0.784800i \(-0.712766\pi\)
−0.619749 + 0.784800i \(0.712766\pi\)
\(588\) 0 0
\(589\) −608.000 −0.0425335
\(590\) 0 0
\(591\) −11418.0 −0.794710
\(592\) 0 0
\(593\) 2802.00 0.194038 0.0970188 − 0.995283i \(-0.469069\pi\)
0.0970188 + 0.995283i \(0.469069\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2568.00 −0.176049
\(598\) 0 0
\(599\) 2664.00 0.181716 0.0908582 − 0.995864i \(-0.471039\pi\)
0.0908582 + 0.995864i \(0.471039\pi\)
\(600\) 0 0
\(601\) 23962.0 1.62634 0.813170 − 0.582026i \(-0.197740\pi\)
0.813170 + 0.582026i \(0.197740\pi\)
\(602\) 0 0
\(603\) −3492.00 −0.235830
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 11940.0 0.798401 0.399201 − 0.916864i \(-0.369288\pi\)
0.399201 + 0.916864i \(0.369288\pi\)
\(608\) 0 0
\(609\) 12360.0 0.822418
\(610\) 0 0
\(611\) 3440.00 0.227770
\(612\) 0 0
\(613\) −16794.0 −1.10653 −0.553265 − 0.833005i \(-0.686618\pi\)
−0.553265 + 0.833005i \(0.686618\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 20706.0 1.35104 0.675520 − 0.737341i \(-0.263919\pi\)
0.675520 + 0.737341i \(0.263919\pi\)
\(618\) 0 0
\(619\) −10724.0 −0.696339 −0.348170 − 0.937432i \(-0.613197\pi\)
−0.348170 + 0.937432i \(0.613197\pi\)
\(620\) 0 0
\(621\) −3672.00 −0.237282
\(622\) 0 0
\(623\) 1320.00 0.0848871
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 672.000 0.0428024
\(628\) 0 0
\(629\) −29892.0 −1.89487
\(630\) 0 0
\(631\) 5744.00 0.362385 0.181193 − 0.983448i \(-0.442004\pi\)
0.181193 + 0.983448i \(0.442004\pi\)
\(632\) 0 0
\(633\) 9060.00 0.568883
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 4902.00 0.304905
\(638\) 0 0
\(639\) 6048.00 0.374421
\(640\) 0 0
\(641\) 27906.0 1.71953 0.859767 − 0.510687i \(-0.170609\pi\)
0.859767 + 0.510687i \(0.170609\pi\)
\(642\) 0 0
\(643\) 20556.0 1.26073 0.630365 − 0.776299i \(-0.282905\pi\)
0.630365 + 0.776299i \(0.282905\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10224.0 −0.621247 −0.310624 − 0.950533i \(-0.600538\pi\)
−0.310624 + 0.950533i \(0.600538\pi\)
\(648\) 0 0
\(649\) −3136.00 −0.189675
\(650\) 0 0
\(651\) −9120.00 −0.549064
\(652\) 0 0
\(653\) 12982.0 0.777986 0.388993 − 0.921241i \(-0.372823\pi\)
0.388993 + 0.921241i \(0.372823\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −10530.0 −0.625288
\(658\) 0 0
\(659\) 1512.00 0.0893766 0.0446883 − 0.999001i \(-0.485771\pi\)
0.0446883 + 0.999001i \(0.485771\pi\)
\(660\) 0 0
\(661\) 16710.0 0.983273 0.491637 − 0.870800i \(-0.336399\pi\)
0.491637 + 0.870800i \(0.336399\pi\)
\(662\) 0 0
\(663\) −27348.0 −1.60197
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −28016.0 −1.62636
\(668\) 0 0
\(669\) 5052.00 0.291961
\(670\) 0 0
\(671\) −112.000 −0.00644368
\(672\) 0 0
\(673\) −7962.00 −0.456036 −0.228018 − 0.973657i \(-0.573225\pi\)
−0.228018 + 0.973657i \(0.573225\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −12226.0 −0.694067 −0.347033 − 0.937853i \(-0.612811\pi\)
−0.347033 + 0.937853i \(0.612811\pi\)
\(678\) 0 0
\(679\) 18520.0 1.04673
\(680\) 0 0
\(681\) −6012.00 −0.338297
\(682\) 0 0
\(683\) −8748.00 −0.490092 −0.245046 − 0.969511i \(-0.578803\pi\)
−0.245046 + 0.969511i \(0.578803\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 15126.0 0.840019
\(688\) 0 0
\(689\) 10836.0 0.599156
\(690\) 0 0
\(691\) 7324.00 0.403210 0.201605 − 0.979467i \(-0.435384\pi\)
0.201605 + 0.979467i \(0.435384\pi\)
\(692\) 0 0
\(693\) 10080.0 0.552536
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −26076.0 −1.41707
\(698\) 0 0
\(699\) −9270.00 −0.501607
\(700\) 0 0
\(701\) −21934.0 −1.18179 −0.590896 − 0.806748i \(-0.701226\pi\)
−0.590896 + 0.806748i \(0.701226\pi\)
\(702\) 0 0
\(703\) 1128.00 0.0605168
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3960.00 −0.210652
\(708\) 0 0
\(709\) −10690.0 −0.566250 −0.283125 − 0.959083i \(-0.591371\pi\)
−0.283125 + 0.959083i \(0.591371\pi\)
\(710\) 0 0
\(711\) −3672.00 −0.193686
\(712\) 0 0
\(713\) 20672.0 1.08580
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 6408.00 0.333767
\(718\) 0 0
\(719\) −13792.0 −0.715375 −0.357688 − 0.933841i \(-0.616435\pi\)
−0.357688 + 0.933841i \(0.616435\pi\)
\(720\) 0 0
\(721\) −30640.0 −1.58265
\(722\) 0 0
\(723\) −294.000 −0.0151231
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −24004.0 −1.22457 −0.612283 − 0.790639i \(-0.709749\pi\)
−0.612283 + 0.790639i \(0.709749\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 43672.0 2.20967
\(732\) 0 0
\(733\) −8562.00 −0.431439 −0.215719 − 0.976455i \(-0.569210\pi\)
−0.215719 + 0.976455i \(0.569210\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −21728.0 −1.08597
\(738\) 0 0
\(739\) 13836.0 0.688722 0.344361 − 0.938837i \(-0.388096\pi\)
0.344361 + 0.938837i \(0.388096\pi\)
\(740\) 0 0
\(741\) 1032.00 0.0511626
\(742\) 0 0
\(743\) −22224.0 −1.09733 −0.548667 − 0.836041i \(-0.684865\pi\)
−0.548667 + 0.836041i \(0.684865\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 6012.00 0.294468
\(748\) 0 0
\(749\) −8880.00 −0.433202
\(750\) 0 0
\(751\) −11544.0 −0.560914 −0.280457 − 0.959867i \(-0.590486\pi\)
−0.280457 + 0.959867i \(0.590486\pi\)
\(752\) 0 0
\(753\) −15120.0 −0.731744
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 3814.00 0.183120 0.0915602 − 0.995800i \(-0.470815\pi\)
0.0915602 + 0.995800i \(0.470815\pi\)
\(758\) 0 0
\(759\) −22848.0 −1.09266
\(760\) 0 0
\(761\) −25662.0 −1.22240 −0.611200 − 0.791476i \(-0.709313\pi\)
−0.611200 + 0.791476i \(0.709313\pi\)
\(762\) 0 0
\(763\) 1240.00 0.0588349
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4816.00 −0.226722
\(768\) 0 0
\(769\) 30658.0 1.43765 0.718827 − 0.695189i \(-0.244679\pi\)
0.718827 + 0.695189i \(0.244679\pi\)
\(770\) 0 0
\(771\) −5958.00 −0.278304
\(772\) 0 0
\(773\) 30894.0 1.43749 0.718745 − 0.695274i \(-0.244717\pi\)
0.718745 + 0.695274i \(0.244717\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 16920.0 0.781212
\(778\) 0 0
\(779\) 984.000 0.0452573
\(780\) 0 0
\(781\) 37632.0 1.72417
\(782\) 0 0
\(783\) 5562.00 0.253857
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 21596.0 0.978163 0.489081 − 0.872238i \(-0.337332\pi\)
0.489081 + 0.872238i \(0.337332\pi\)
\(788\) 0 0
\(789\) −4248.00 −0.191677
\(790\) 0 0
\(791\) −8280.00 −0.372191
\(792\) 0 0
\(793\) −172.000 −0.00770227
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 8646.00 0.384262 0.192131 − 0.981369i \(-0.438460\pi\)
0.192131 + 0.981369i \(0.438460\pi\)
\(798\) 0 0
\(799\) 4240.00 0.187735
\(800\) 0 0
\(801\) 594.000 0.0262022
\(802\) 0 0
\(803\) −65520.0 −2.87939
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 20010.0 0.872844
\(808\) 0 0
\(809\) 24954.0 1.08447 0.542235 − 0.840227i \(-0.317578\pi\)
0.542235 + 0.840227i \(0.317578\pi\)
\(810\) 0 0
\(811\) −40004.0 −1.73210 −0.866048 − 0.499960i \(-0.833348\pi\)
−0.866048 + 0.499960i \(0.833348\pi\)
\(812\) 0 0
\(813\) 144.000 0.00621193
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −1648.00 −0.0705707
\(818\) 0 0
\(819\) 15480.0 0.660458
\(820\) 0 0
\(821\) 16570.0 0.704381 0.352191 − 0.935928i \(-0.385437\pi\)
0.352191 + 0.935928i \(0.385437\pi\)
\(822\) 0 0
\(823\) −4388.00 −0.185852 −0.0929259 − 0.995673i \(-0.529622\pi\)
−0.0929259 + 0.995673i \(0.529622\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 14364.0 0.603972 0.301986 − 0.953312i \(-0.402350\pi\)
0.301986 + 0.953312i \(0.402350\pi\)
\(828\) 0 0
\(829\) −21170.0 −0.886929 −0.443465 − 0.896292i \(-0.646251\pi\)
−0.443465 + 0.896292i \(0.646251\pi\)
\(830\) 0 0
\(831\) 20814.0 0.868868
\(832\) 0 0
\(833\) 6042.00 0.251312
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −4104.00 −0.169480
\(838\) 0 0
\(839\) −10664.0 −0.438811 −0.219405 − 0.975634i \(-0.570412\pi\)
−0.219405 + 0.975634i \(0.570412\pi\)
\(840\) 0 0
\(841\) 18047.0 0.739965
\(842\) 0 0
\(843\) 5082.00 0.207632
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 36100.0 1.46448
\(848\) 0 0
\(849\) 19092.0 0.771774
\(850\) 0 0
\(851\) −38352.0 −1.54488
\(852\) 0 0
\(853\) 3190.00 0.128046 0.0640232 − 0.997948i \(-0.479607\pi\)
0.0640232 + 0.997948i \(0.479607\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −20814.0 −0.829630 −0.414815 − 0.909906i \(-0.636154\pi\)
−0.414815 + 0.909906i \(0.636154\pi\)
\(858\) 0 0
\(859\) 18988.0 0.754205 0.377103 − 0.926172i \(-0.376920\pi\)
0.377103 + 0.926172i \(0.376920\pi\)
\(860\) 0 0
\(861\) 14760.0 0.584227
\(862\) 0 0
\(863\) 11664.0 0.460078 0.230039 − 0.973181i \(-0.426115\pi\)
0.230039 + 0.973181i \(0.426115\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −18969.0 −0.743046
\(868\) 0 0
\(869\) −22848.0 −0.891905
\(870\) 0 0
\(871\) −33368.0 −1.29808
\(872\) 0 0
\(873\) 8334.00 0.323096
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 8246.00 0.317500 0.158750 − 0.987319i \(-0.449254\pi\)
0.158750 + 0.987319i \(0.449254\pi\)
\(878\) 0 0
\(879\) −9402.00 −0.360775
\(880\) 0 0
\(881\) 22890.0 0.875350 0.437675 − 0.899133i \(-0.355802\pi\)
0.437675 + 0.899133i \(0.355802\pi\)
\(882\) 0 0
\(883\) 33548.0 1.27857 0.639287 − 0.768969i \(-0.279230\pi\)
0.639287 + 0.768969i \(0.279230\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −32264.0 −1.22133 −0.610665 − 0.791889i \(-0.709098\pi\)
−0.610665 + 0.791889i \(0.709098\pi\)
\(888\) 0 0
\(889\) −19920.0 −0.751513
\(890\) 0 0
\(891\) 4536.00 0.170552
\(892\) 0 0
\(893\) −160.000 −0.00599574
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −35088.0 −1.30608
\(898\) 0 0
\(899\) −31312.0 −1.16164
\(900\) 0 0
\(901\) 13356.0 0.493843
\(902\) 0 0
\(903\) −24720.0 −0.910997
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 51228.0 1.87541 0.937706 − 0.347431i \(-0.112946\pi\)
0.937706 + 0.347431i \(0.112946\pi\)
\(908\) 0 0
\(909\) −1782.00 −0.0650222
\(910\) 0 0
\(911\) 2144.00 0.0779735 0.0389868 − 0.999240i \(-0.487587\pi\)
0.0389868 + 0.999240i \(0.487587\pi\)
\(912\) 0 0
\(913\) 37408.0 1.35600
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 5280.00 0.190143
\(918\) 0 0
\(919\) −33584.0 −1.20548 −0.602739 − 0.797939i \(-0.705924\pi\)
−0.602739 + 0.797939i \(0.705924\pi\)
\(920\) 0 0
\(921\) 708.000 0.0253305
\(922\) 0 0
\(923\) 57792.0 2.06094
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −13788.0 −0.488519
\(928\) 0 0
\(929\) −3590.00 −0.126786 −0.0633929 − 0.997989i \(-0.520192\pi\)
−0.0633929 + 0.997989i \(0.520192\pi\)
\(930\) 0 0
\(931\) −228.000 −0.00802621
\(932\) 0 0
\(933\) 11328.0 0.397494
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 21686.0 0.756084 0.378042 − 0.925788i \(-0.376597\pi\)
0.378042 + 0.925788i \(0.376597\pi\)
\(938\) 0 0
\(939\) −23754.0 −0.825540
\(940\) 0 0
\(941\) −5174.00 −0.179243 −0.0896215 − 0.995976i \(-0.528566\pi\)
−0.0896215 + 0.995976i \(0.528566\pi\)
\(942\) 0 0
\(943\) −33456.0 −1.15533
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 35524.0 1.21898 0.609490 − 0.792793i \(-0.291374\pi\)
0.609490 + 0.792793i \(0.291374\pi\)
\(948\) 0 0
\(949\) −100620. −3.44179
\(950\) 0 0
\(951\) 13086.0 0.446207
\(952\) 0 0
\(953\) 16122.0 0.547999 0.273999 − 0.961730i \(-0.411653\pi\)
0.273999 + 0.961730i \(0.411653\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 34608.0 1.16898
\(958\) 0 0
\(959\) −45560.0 −1.53411
\(960\) 0 0
\(961\) −6687.00 −0.224464
\(962\) 0 0
\(963\) −3996.00 −0.133717
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 19188.0 0.638102 0.319051 − 0.947738i \(-0.396636\pi\)
0.319051 + 0.947738i \(0.396636\pi\)
\(968\) 0 0
\(969\) 1272.00 0.0421698
\(970\) 0 0
\(971\) 38464.0 1.27123 0.635617 − 0.772004i \(-0.280746\pi\)
0.635617 + 0.772004i \(0.280746\pi\)
\(972\) 0 0
\(973\) −36240.0 −1.19404
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 43930.0 1.43853 0.719266 − 0.694735i \(-0.244478\pi\)
0.719266 + 0.694735i \(0.244478\pi\)
\(978\) 0 0
\(979\) 3696.00 0.120659
\(980\) 0 0
\(981\) 558.000 0.0181606
\(982\) 0 0
\(983\) 17328.0 0.562235 0.281118 − 0.959673i \(-0.409295\pi\)
0.281118 + 0.959673i \(0.409295\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −2400.00 −0.0773990
\(988\) 0 0
\(989\) 56032.0 1.80153
\(990\) 0 0
\(991\) 18160.0 0.582110 0.291055 − 0.956706i \(-0.405994\pi\)
0.291055 + 0.956706i \(0.405994\pi\)
\(992\) 0 0
\(993\) 23940.0 0.765068
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 9102.00 0.289131 0.144565 − 0.989495i \(-0.453822\pi\)
0.144565 + 0.989495i \(0.453822\pi\)
\(998\) 0 0
\(999\) 7614.00 0.241137
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1200.4.a.p.1.1 1
4.3 odd 2 600.4.a.i.1.1 1
5.2 odd 4 1200.4.f.t.49.2 2
5.3 odd 4 1200.4.f.t.49.1 2
5.4 even 2 240.4.a.g.1.1 1
12.11 even 2 1800.4.a.f.1.1 1
15.14 odd 2 720.4.a.q.1.1 1
20.3 even 4 600.4.f.a.49.2 2
20.7 even 4 600.4.f.a.49.1 2
20.19 odd 2 120.4.a.b.1.1 ✓ 1
40.19 odd 2 960.4.a.bj.1.1 1
40.29 even 2 960.4.a.k.1.1 1
60.23 odd 4 1800.4.f.v.649.2 2
60.47 odd 4 1800.4.f.v.649.1 2
60.59 even 2 360.4.a.n.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.4.a.b.1.1 ✓ 1 20.19 odd 2
240.4.a.g.1.1 1 5.4 even 2
360.4.a.n.1.1 1 60.59 even 2
600.4.a.i.1.1 1 4.3 odd 2
600.4.f.a.49.1 2 20.7 even 4
600.4.f.a.49.2 2 20.3 even 4
720.4.a.q.1.1 1 15.14 odd 2
960.4.a.k.1.1 1 40.29 even 2
960.4.a.bj.1.1 1 40.19 odd 2
1200.4.a.p.1.1 1 1.1 even 1 trivial
1200.4.f.t.49.1 2 5.3 odd 4
1200.4.f.t.49.2 2 5.2 odd 4
1800.4.a.f.1.1 1 12.11 even 2
1800.4.f.v.649.1 2 60.47 odd 4
1800.4.f.v.649.2 2 60.23 odd 4